In
The Ecological Approach, Gibson is keen to move away from the concepts and quantities of physics, and perhaps geometry, as useful theoretical apparatus for vision science. So, for example, in the summary for Chapter 1, he writes,
SUMMARY
The environment of animals and men is what they perceive. The environment is not the same as the physical world, if one means by that the world described by physics.
The observer and his environment are complementary. So are the set of observers and their common environment.
The components and events of the environment fall into natural units. These units are nested. They should not be confused with the metric units of space and time.
The environment persists in some respects and changes in other respects. The most radical change is going out of existence or coming into existence.
Turvey & Carello, 1986, say similar sorts of things:
Fig. 1.1. In conventional discussions of space perception, 'space' is a mathematical concept. Theory and experiments focus on how an observer perceives points, distances between points and motions of points localized by triplets of values in a Cartesian coordinate system. The mathematical conception of space is traditional and, perhaps, convenient but it has little bearing on what animals (including humans) need to perceive in order to get around successfully in their cluttered environment. (Turvey & Carello, 1986, p. 133).
Runeson, for his part, however, does not seem to abide by this prohibition on the concepts and quantities of physics and geometry. For example, he writes,
Geometrically, the chances that an equivalent configuration would occur by random is therefore only in a 100 million and that is for a very simple, barren case. For a room without the size restriction or with furniture and structured surfaces, the chances are many orders of magnitude smaller yet.
Physical constraints. Solid chunks of matter can not be distributed arbitrarily in space, especially not in a gravitational field. Hence, out of the total set of geometrically possible configurations, only a subset can be physically realized (Todd, 1985). The subset that can be realized through more or less natural shaping processes is even smaller. The physical constraints that apply to the manufacture of roomlike enclosures include gravity and other load forces, strength and weight of materials, methods for shaping and joining parts, economy of space, materials, and labor. One must then ask, do prevailing physical and ecological constraints suffice to exclude the kind of room shapes that would be projectively equivalent with normal rooms? (Runeson, 1988, p. 299).
Personally, I like Runeson's approach, because it is more familiar to me.
